Monday, December 27, 2010

Rebel1 wrote: @Victor Reppert: You completely missed the point, once again. YOU DON'T HAVE THE RIGHT TO USE THE WORD "BAYESIAN". It's a term that has a clear meaning in Mathematics, and it is clearly not the one you imagine. Is that clear enough, now that I've used ALL CAPS??? Bayes' Theorem REQUIRES quantifiable prior probabilities to have any meaning, especially when those probabilities are likely to be low. And miracles are not miracles if they are not highly improbable.

The very point made by many of your critics remain. If miracles exist, then they will be resistant to any sort of probabilistic analysis. You cannot steal the language of Mathematics to give your personal, unvalidated beliefs the credibility attached to that field. You are not even a philosopher, because I expect from philosophers a little rigour in their use of language.

What you are, is a hack, no better than Deepak Chopra when he uses the word Quantum to give his pablum a "sciency" air.

So stop using the word "Bayesian", and we might be able to have a conversation. Use the word, and all you'll get from people who actually know what the word means is ridicule.

VR: You might want to read John Earman's (University of Pittsburgh philosopher of science and an atheist, and Keith's former teacher) book "Hume's Abject Failure" before you accuse me of not knowing what the word Bayesian means. (He references one of my papers in his book). Or you might try convincing my philosophy of science teacher at the University of Illinois, Patrick Maher (author of books like Betting On Theories), who worked with me on Bayesian theory while I was getting my doctorate, and explain to him that I don't know anything about Bayesianism. If Jordan Howard Sobel were still alive, you might want to ask him also, since he read two of my papers, and found them reasonable efforts, even though he differed with my conclusions and is the leading defender of the Bayesianized version of Hume's argument against miracles. Or, you can ask Keith. NONE of these people believe in miracles, but all of them thought I made some reasonable points in my two papers, one which appears on Internet Infidels, and the other of which came out in International Journal for Philosophy of Religion in 1989.

You might also want to read up on the Personalist school of Bayesian prior probabilities, a school that has many adherents. You might want to read Colin Howson and Peter Urbach's Scientific Inference: A Bayesian Approach, before you dismiss personalism as hogwash.

You might also try examining my arguments in my Infidels paper on miracles against frequentism before you make charges like this.

You also might want to think twice about the fact that you completely misrepresented my position before you blast me into the outer darkness for a complete misunderstanding of Bayesianism. In short, you might want to do your homework.

The fact that Bayesian inference is used with certain conventions within your scientific enterprise doesn't mean that you can dismiss the work of many other people who use that same methodology in different contexts, with different ground rules. To me, Bayesian personalism isn't a way of claiming a kind of mathematical precision for beliefs about, say, the resurrection which I know to be impossible. It is an attempt on my part to think from the standpoint of a model which allows a plurality of antecedent probabilities to start with, but nevetheless leaves people open to the consideration of evidence for and against religious beliefs. It's the best model I know of to do this job.

I could be thoroughly misguided, but I think I can appeal to the authority of some people who know a lot more about Bayesianism than I do to show that I do know what Bayesianism is.

The arguments here are all controversial. However the "that isn't how I use Bayes in my day job" objection is infuriatingly common and completely specious.

The only effective reply is - "this is how many other people use Bayes in their day job. If you wish to object to this use of Bayes Theorem you will have to use arguments, and stop trying to smuggle positivism in through the back door."

I get a little tired of being called a hack for espousing a position about which there is a standard literature, especially when I take what looks at this point like the mainstream position.

There is a "standard" literature on Hume, Bayes, and Miracles. The "mainstream" is found in John Earman's book Hume's Abject Failure. I'm not saying there aren't, and can't be dissent from that position, but the guy's a University of Pittsburgh philosopher of science for crying out loud. He doesn't have a religious axe to grind, since he's not a believer. If you want to take a different position from him you'd better have an answer for him. It's pretty much the epistemological conclusions that Patrick Maher and I came to when we worked on the same issue at the U of I. Pat is an atheist who thinks no miracles have ever occurred, and I am a Christian, but it was remarkable how much we could agree on the epistemology and Bayesian theory surrounding the issue.

The poster also seemed to know nothing about Bayesian personalism, which is a major position in the Bayesian theory of antecedent probabilities.

I think I will do a walk-through of Earman's overall argument, so that people can understand it. I actually think William Lane Craig, who appealed to Earman in his debate with Bart Ehrman (try keeping those names straight!) papered over some aspects of Earman's position.

Would Tim be able to say a thing or two about this issue? The general objection seems to be that Bayes cannot - or should not - be used in the absence of hard statistical data.

This seems to be a positivist interpretation of frequentism. I'm not sure that those using Bayesian Networks to develop expert systems would want to commit themselves to this position. Some subjectivity seems inescapable in making judgements about probabilities. As you have pointed out, there is no non-controversial way to resolve the reference class problem.And as I've pointed out this objection rests on the objectors ignorance of how Bayes is used outside their area of expertise! It's very shoddy work on the objectors part.

I got into some discussions with Tim on this a long time ago. Tim really doesn't like personalism about priors' he does think they should have some grounding. However I don't think he's a pure frequentist, and he doesn't go for the positivism that people like the secular outpost commentator want to impose.

Reading Earman, I think I prefer to set the whole personalist-anti-personalist debate aside by introducing the idea of pluralism about prior probabilities. If you start talking like a personalist people start getting the idea that you are just starting from wherever your personal biases have taken you, while for most of us who have reflected about religion and the philosophy of religion, our prior for miracle claims is going to be fed into by such things as the credibility of theism, the moral credibility of Jesus and Christianity, our sense of whether Christians are right about what humans most profoundly need, etc. Indeed, another part of it would be whether the miracles attributed to Jesus are ones that appropriate fit with the concept of God. All of this stuff is tough to quantify, and as a result you have to just deal with the fact that people will be looking at evidence for and against Christian miracles informed by very different perspectives. Even though Hume didn't prove that we should look at the evidence essentially epistemically closed to the miraculous, his opponents have not proved that everyone has to come to this discussion with priors that will allow them to be genuinely open-minded about being persuaded to accept these miracle reports. So what I like to do is to "bracket" the left side of the equals sign in Bayes' theorem, on the assumption that of course people with lots of different priors are going to be looking at this, and just concentrate on the right side of the equals sign. Is there anything in the evidence that ought to surprise a skeptic who is paying attention. If there is, and it makes sense from a Christian standpoint, then I figure I've got something that will pull the skeptic in the direction of Christianity, even though his priors may be such that it won't come anywhere near to convincing him that Christianity is true.

Although I'm not an expert, I agree with your "pluralist" (or what Hacking would call "eclectic") approach. Again, when it comes to priors, I think a lot of people associate personalism with "subjectivism" and "anything goes". But I think that personalists can look an objective criteria when making a judgement about priors. (A big problem here is that "subjective" probabilities means different things to different writers. Funnily enough, when I mentioned to a friend that some subjectivity seems inevitable, he reacted as if I'd questioned the Virgin birth. When I made it clear that I wasn't endorsing anything like subjectivism or relativism, he calmed down. The word "subjective" seems to have an unsettling effect on the stablest of minds!

Vic's representation of my views is fair. I think there are some rational constraints on priors, and frequency data provide one source for some such constraints, but they are certainly not the only source. (Think symmetry.)

I'm a total amateur - but I would prefer to put some rational constraints on priors. Frequency data is one constraint (as you say Tim). I think that Lydia McGrew uses this very effectively in her response to Sober's critique of design arguments (although the discussion there is about likelihoods and not priors).

But this "Rebel" chappy who attacked Tim seems to think that we need precisely quantified frequencies gained by empirical observation or the prior is meaningless! (My assumption is that he is thinking of Bayesian statistics) And this seems to be a common objection on Internet discussions. I've seen Swinburne's work dismissed on these grounds several times.

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About Me

I am the author of C. S. Lewis's Dangerous Idea: In Defense of the Argument from Reason, published by Inter-Varsity Press. I received a Ph.D in philosophy from the University of Illinois at Urbana-Champaign in 1989.